{"title":"Representations of cyclotomic rational Cherednik algebras with aspherical parameters","authors":"Huijun Zhao","doi":"10.17760/d20291522","DOIUrl":null,"url":null,"abstract":"In this article, we describe all two sided ideals of a cyclotomic rational Cherednik algebra $H_\\mathbf{c}$ and its spherical subalgebra $eH_\\mathbf{c} e$ with a Weil generic aspherical parameter $\\mathbf{c}$, and further describe the simple modules in the category $\\mathcal{O}^{sph}_\\mathbf{c}$ . The main tools we use are categorical Kac-Moody actions on catogories $\\mathcal{O}_\\mathbf{c}$ and restriction functors for Harish-Chandra bimodules.","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"193 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17760/d20291522","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we describe all two sided ideals of a cyclotomic rational Cherednik algebra $H_\mathbf{c}$ and its spherical subalgebra $eH_\mathbf{c} e$ with a Weil generic aspherical parameter $\mathbf{c}$, and further describe the simple modules in the category $\mathcal{O}^{sph}_\mathbf{c}$ . The main tools we use are categorical Kac-Moody actions on catogories $\mathcal{O}_\mathbf{c}$ and restriction functors for Harish-Chandra bimodules.
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